The sum of two numbers is 30. One exceeds the other by 15. What are the two numbers?​

the fireworks will be 612 feet high when it explodes.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, Pyrotechnicians can use polynomials to plan complex fireworks displays. A firework is launched from a platform 6 feet above the ground at a speed of 200 feet per second.

Expression that represents the height of firework = -16t² + 200t + 6

Since The firework has a 5-second fuse.

Thus, the firework will explode at t = 5

So, height at t= 5:

height of firework = -16 * 5² + 200*5 +6

height of firework = -16 * 25  + 1000 +6

height of firework = - 400 + 1000 + 6

Height of firework = 606

Since it started at 6 feet height

Thus total height at firework starts = 606 +6

total height at firework starts = 612

Therefore, the firework will explode at 612 feet in height.

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Number of quarters is 6 and number of nickels are 42.

One eighth of Al's coins are quarters, so if we let x be the total number of coins, then x/8 is the number of quarters Al has.

We know that:

Quarters are worth $0.25 and nickels are worth $0.05 and total value of the coins is $3.60

so, x/8 * $0.25 + (x-x/8) * $0.05 = $3.60

=> x/8 * 0.25 + 7x/8 * 0.05 = 3.60

multiplying both sides by 8 to cancel out 8, we get

=> x*0.25 + 7x * 0.05 = 28.8

=> x/4 + 7x/20 = 28.8

=> (5x + 7x)/20 = 28.8

=> 12x = 576

=> x= 48

x/8 = 6 and (x-x/8) = 42

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The number line which best conveys Gregg's situation is B.

line B is the answer and the image is attached,

Since Greg has calculated that his least or minimum speed should be 50 miles per hour ,

Then the line starts at 50 with the starting point shaded due to the at least notation.

Then at least means that,

Gregg may need to travel at a higher speed than 50, so the direction of the arrow moves to the right of the number line depicting a possible increase in Gregg's speed.

Therefore, the number line which best conveys Gregg's situation is B.

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The value of w in the rhombus is 19 degrees

From the question, we have the following parameters that can be used in our computation:

Angle CFD = 2w

Angle FED = 52 degrees

The figure is a rhombus

using the above as a guide, we have the following:

2w + 52 = 90

This is so because the angles in the base of the individual triangle are equal

Evaluate the like terms

2w = 38

Divide by 2

w = 19

hence, the solution is w = 19

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Part A:

Find m∠2,

Since ∠1 and ∠2 are alternate interior angles, they are equal. So, m∠2=60°

Part B:  

Find m∠3,

Since ∠2 and∠3 are supplementary, the sum of their measures is 180°. So, m∠3=180°-60° which is 120°.

62 points, he would need to improve his credit score in order to take a mortgage for $150,000.

What is a mortgage?

It is an agreement between you and a lender that allows you to borrow money to purchase or refinance a home and gives the lender the right to take your property if you fail to repay the money you've borrowed. A mortgage is a type of loan that's used to finance the property. A mortgage is a type of loan, but not all loans are mortgages. Mortgages are “secured” loans.

To calculate the monthly payment, we can use the formula:

M = P [i(1 + i)^n] / [(1 + i)^n – 1]

Where M is the monthly payment, P is the loan amount, i is the interest rate, and n is the number of payments (in this case, the number of months in 30 years)

Plugging in the values,

M = 150000 * (0.0929 / 12) / [ (1 + (0.0929 / 12))^(12 * 30) - 1]

This gives a monthly payment of $1238.

To find out how many points he needs to improve his credit score, we can compare this monthly payment to the maximum monthly payment he can afford, which is $14,000.

If $1238 is more than $14,000, he would need to improve his credit score to a point where the monthly payment would be less than $14,000. By looking at the table, we can see that the interest rate for credit score of 620-674 is 7.40%.

Hence, (D) option is the correct answer.

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If the pizza is divided in to four equal parts , then each equal part is named as "one fourth" .

The fraction is defined as a numerical value that is part of a whole. Fraction is evaluated by dividing a whole into number of parts.

For Example : 1/2 represents the half part of the whole .

The pizza is divided into four equal part ;

So , the total number of parts in the pizza is = 4 parts ,

one part of the pizza will be written in fraction form as : 1/4 ;

We can say that each pizza slice is 1/4 of whole pizza and  1/4 is read out  as "one fourth".

The given question is incomplete , the complete question is

What fraction names the 4 equal parts of the whole pizza ?

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Approximately 81.5% of the respondent will be between 64.29 and 93.54 years old.

Given that:

Mean u = 74.04

Standard deviation S.D. = 9.75

Distribution of ages is mound-shaped and symmetric.

We have to find percentage of the respondent between 64.29 and 93.54 years old.

For 93.54

z-score = [tex]\frac{x-u}{S.D}[/tex]

Z score = (93.54 – 74.04)/9.75 = 19.5/9.75 = 2

For 64.29

Z score = (64.29 – 74.04)/9.75 = -9.75/9.75 = -1

Now p-value from z-table:

P(x<93.54) = p(z<2) = 0.97725

P(x>64.29) = p(z>-1) = 0.15866

Probability between 64.29 and 93.54 year old = .97725 – 0.15865

= 0.8186

Percentage of the respondent = 0.8186 * 100 = 81.8%

Therefore, approximately 81.5% of the respondent will be between 64.29 and 93.54 years old.

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Answer: The formula for population growth of bacteria with a constant doubling time is P = Po*2^(t/d), where P is the population after t hours, Po is the initial population, t is the time in hours, and d is the doubling time.

Given the initial population of 8600 bacteria and a doubling time of 5 hours, we can substitute these values into the formula:

P = 8600 * 2^(7/5)

To find the population after 7 hours, to the nearest whole number, we can use a calculator to calculate 2^(7/5) which is approximately 3.7 and then multiply it with the initial population.

P = 8600*3.7

P = 31420

So, the population of bacteria in the culture after 7 hours will be around 31420.

Step-by-step explanation:

Answer: 4 in

Step-by-step explanation:

The length of the longest side is solved to be 3.76 cm

An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0.

The perimeter o the quadrilateral have a formula that add all the sides together, assuming the factor of the original length is x, the perimeter is solved by

9.6 = 3x + 5x + 6x + 9x

9.6 = 23x

x = 9.6 / 23

x = 0.4174

The length of the longest side

= 9x

= 9 * 0.4174

= 3.76 cm

3.76 cm is the length of the longest side

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Answer: 599 times

Step-by-step explanation: 3594/6=599

Answer: No they are not.

Step-by-step explanation:

1/2x and -5/8x are like terms, if subtracted you get 1 1/8x. But then you are left with an unlike term, 3/4 so your first equation would equal out to 1 1/8x + 3/4

Now for equation 2, you use your distributive property and get 1/8(x)=1/8x

Then you must distribute 1/8(1)=1/8

1/8x + 1/8

So, 1 1/8x + 3/4 ≠ 1/8x + 1/8

Answer:(8 x r)+(8 x 1)

Step-by-step explanation:

[tex]8(r+1)[/tex]

Distribute:

[tex](8)(r)+(8)(1)[/tex]

[tex]\fbox{8r + 8}[/tex]

The total dinner bill was $177.90 including a tip of 20%.

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%"

Given that, a restaurant adds a 20% gratuity (or tip), a dinner bill for a large party comes to $148.25, we need to find the total dinner bill with tip.

The total bill will be = 148.25 + 20% of 148.25

= 148.25 + 20/100 × 148.25

= 148.25 + 0.2 × 148.25

= 148.25 + 29.65

= 177.90

Hence, the total dinner bill was $177.90 including a tip of 20%.

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The cost to rent each chair and table, based on the total cost to the party rental company, is:

Let x be the cost of renting one chair and y be the cost of renting one table.

From the first piece of information given, we can write the equation:

3x + 2y = 25

From the second piece of information given, we can write the equation:

5x + 6y = 65

Solving these equations using elimination gives:

3x + 2y = 25

5x + 6y = 65

15x + 10y = 125

15x + 18y = 195

Subtracting gives:

0x + 8y = 70

y = $ 8.75

The cost to rent a chair is:

3x + 2 (8.75) = 25

3x + 17.5 = 25

3x = 7.5

x = $ 2.5

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Answer:

58

Step-by-step explanation:

error: 64+2p = 180.  he missed 1 p.

so 2p =180-64

p = 58

I year of weekends= 105days therefore 105, therefore you need 105 ice cream bars? hoped this helped

The length of the room are y2 – 5y = 750 , y(y – 5) + 750 = 0 and (y + 25)(y – 30) = 0

it is important to note that the formula for calculating the area of a rectangle is expressed as;

A = lw

Such that;

From the information given, we have that;

Length = y

Width = y - 5

Area = 750 square feet

Substitute the values into the formula

750 =y(y - 5)

expand the bracket

750 = y² - 5y

y² - 5y- 750 = 0

This is factorized to give;

(y + 250 (y - 30)

Hence, the expression is y² - 5y- 750 = 0

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The number of cups of soda Sidney will use for 15 cups of ice cream is 45 cups of soda.

The ratio shows how many times one value is contained in another value.

Example:

There are 3 apples and 2 oranges in a basket.

The ratio of apples to oranges is 3:2 or 3/2.

We have,

From the table,

3.5 cups of ice cream = 10.5 cups of soda.

This means,

1 cup of ice cream = 3 cups of soda.

Multiply 15 on both sides.

15 cups of ice cream = 45 cups of soda.

Thus,

45 cups of soda are used.  

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Answer:

b) 30°

Additional information:-

Step-by-step explanation:

We know that,

→ The other two angles of the isosceles triangles are equal.

Formula we use,

→ <A + <B + <C = 180°

Forming the equation,

→ 120° + x + x = 180°

Now the value of x will be,

→ 120° + x + x = 180°

→ 120° + 2x = 180°

→ 2x = 180° - 120°

→ 2x = 60°

→ x = 60°/2

→ [ x = 30° ]

Hence, option (b) is correct.

[tex]\dfrac{k}{0.1} =36[/tex]

Multiply both sides by 0.1:

[tex](\dfrac{k}{0.1} )\times0.1=(36)\times0.1[/tex]

[tex]\fbox{k = 3.6}[/tex]

As per the collinear point, the common endpoint is called the vertex of the angle, and the rays are called the sides of the angle.

The term collinear point in math is defined as a set of three or more points that exist on the same straight line

Here we have given that an angle is two collinear rays with a common endpoint.

And we need to find an example that contradicts this definition.

Here we also know that an angle is the union of two noncollinear rays with a common endpoint.

Then the common endpoint is called the vertex of the angle and the rays are called the sides of the angle.

And it is measure of an angle is a number representing the spread of the two arms of the angle.

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Answer:

A.9^2+15^2=x^2

Step-by-step explanation:

Pythagorean Theorem

a^2+b^2=c^2

AS per the concept of reasoning, the statement written symbolically is ~Q

The term reasoning in math is defined as a drawing logical conclusions based on evidence or stated assumptions

While we looking into the statement P and Q, then we can  get it as

p: Brad Pitt is governor.

q: There are not 51 states in the U. S.

Here we have to know that the we have to write the following in the symbolic form, that is written as,

=> There are 51 states in the U. S.

While we looking into the statement, we have identified that the  statement is write as the inverse form of the previously given one.

So, the symbolic form is ~Q.

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Answer:

C

Step-by-step explanation:

This looks like a case of multiplying the number of X's by the respective number below it.

For example: the 1/2 has 3 X's, so we multiple (1/2)(3), making it (3/2) or 1.5

Next is the 1 having 2 X's, so (2)(1) is 2

Continuing that trend we get the following

1.5, 4, 2.5, and 3.

So all of our totals are 1.5, 2, 1.5, 4, 2.5, and 3.

Our last step will be adding all these answers together.

1.5 + 2 = 3.5

+ 1.5 = 6

+ 4 = 10

+ 2.5 = 12.5

and finally +3 = a grand total of 15.5 or 15 1/2

Answer:

780

Step-by-step explanation: The answer is 780!

Answer:

The remaining distance will be "56 km".

Step-by-step explanation:

Speed and Time:

The speed (s) of an object seems to be the rate at which it travels from one location to some other. It's also calculated by dividing the distance (d) traveled by the timeframe (t) or duration.

According to the question,

Average speed when cross a late, 108 km/h

On particular day, average speed 94 km/h

Time taken, 4 hours

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^^^^^^

not my work

where I found the answer